Refresher - MATHEMATICS Quiz 17
PROBLEM 1:
A company makes three types of hammers—good, better, and best. The cost of making
each type of hammer is $4, $6, and $7, respectively, and the hammers sell for $6, $9, and
$12. Each day, the cost of making 100 hammers is $520, and the daily revenue from their
sale is $810. How many of each type are manufactured?
Solution:
x = number of good hammers
y = better hammers
z = best hammers
➊ x + y + z = 100
➋ 4x + 6y + 7z = 520
➌ 6x + 9y + 12z = 810
➊ and ➋
➊ 7x + 7y + 7z = 700 by 7
➋ 4x + 6y + 7z = 520
➍ + 3x + y = 180
➊ and ➌
➊ 12x + 12y + 12z = 1,200
➌ 6x + 9y + 12z = 810
6x + 3y = 390
➎ 2x + y = 130
➍ and ➎ y = 180 – 50(3)
3x + y = 180 y = 30
2x + y = 130
x = 50
z = 100 – 80
z = 20
The company makes 50 good hammers, 30 better hammers, and 20 best hammers each
day.
, Refresher - MATHEMATICS Quiz 17
PROBLEM 2:
A shell is fired from a ground level with an initial speed of 768 ft/sec. at an angle
of 30˚. Find the vector function of the shell’s trajection and parametric equations
of the shell’s trajectory.
Solution:
Vo = 768 Cos 30˚ i + 768 Sin 30˚ j
Vo = 384 3 i + 384 j
Acceleration of gravity in vector form:
a(t) = - gt - 32t
V(t) = 384 3 i + (- 32t + 384)j
Integrating the velocity V(t)
( ) ⎛ 32t 2
r(t) = 384 3 t i + ⎜ -
⎝ 2
⎞
+ 384t ⎟ j
⎠
r(t) = ( 384 3 t ) i + ( - 16t 2
)
+ 384t j (vector function)
Parametric equations of the shell's trajectory
x(t) = 384 3 t
y(t) = - 16t 2 + 384t
PROBLEM 1:
A company makes three types of hammers—good, better, and best. The cost of making
each type of hammer is $4, $6, and $7, respectively, and the hammers sell for $6, $9, and
$12. Each day, the cost of making 100 hammers is $520, and the daily revenue from their
sale is $810. How many of each type are manufactured?
Solution:
x = number of good hammers
y = better hammers
z = best hammers
➊ x + y + z = 100
➋ 4x + 6y + 7z = 520
➌ 6x + 9y + 12z = 810
➊ and ➋
➊ 7x + 7y + 7z = 700 by 7
➋ 4x + 6y + 7z = 520
➍ + 3x + y = 180
➊ and ➌
➊ 12x + 12y + 12z = 1,200
➌ 6x + 9y + 12z = 810
6x + 3y = 390
➎ 2x + y = 130
➍ and ➎ y = 180 – 50(3)
3x + y = 180 y = 30
2x + y = 130
x = 50
z = 100 – 80
z = 20
The company makes 50 good hammers, 30 better hammers, and 20 best hammers each
day.
, Refresher - MATHEMATICS Quiz 17
PROBLEM 2:
A shell is fired from a ground level with an initial speed of 768 ft/sec. at an angle
of 30˚. Find the vector function of the shell’s trajection and parametric equations
of the shell’s trajectory.
Solution:
Vo = 768 Cos 30˚ i + 768 Sin 30˚ j
Vo = 384 3 i + 384 j
Acceleration of gravity in vector form:
a(t) = - gt - 32t
V(t) = 384 3 i + (- 32t + 384)j
Integrating the velocity V(t)
( ) ⎛ 32t 2
r(t) = 384 3 t i + ⎜ -
⎝ 2
⎞
+ 384t ⎟ j
⎠
r(t) = ( 384 3 t ) i + ( - 16t 2
)
+ 384t j (vector function)
Parametric equations of the shell's trajectory
x(t) = 384 3 t
y(t) = - 16t 2 + 384t
